For screens, IPA and a microfiber cloth or kimwipe usually works great. I use isopropyl alcohol to clean lots of stuff, but it wouldn’t be my goto for the body of a kindle.

Since it’s probably mostly finger grime, I think a slightly damp microfiber cloth with a bit of dish soap would work best. You can then rinse the cloth to remove the soap. Wring the cloth to remove most of the water then use it to remove any trace of soap on the device.
That’s how I clean my keyboard’s wrist piece.

Obvious warnings: don’t submerge the device, don’t put it under running water.